Ответ:

Производная степенной функции :  [tex]\bf (x^{n})'=n\cdot x^{n-1}\ \ ,\ \ \sqrt[n]{x^{k}}=x^{\frac{k}{n}}[/tex]  .

[tex]\bf f(x)=3\sqrt[3]{\bf x}-10\sqrt[5]{\bf x}=3x^{\frac{1}{3}}-10x^{\frac{1}{5}}\ \ ,\ \ \ x_0=1\\\\f'(x)=3\cdot \dfrac{1}{3}\, x^{-\frac{2}{3}}-10\cdot \dfrac{1}{5}\, x^{-\frac{4}{5}} =\dfrac{1}{\sqrt[3]{\bf x^2}}-\dfrac{2}{\sqrt[5]{\bf x^4}}\\\\f'(1)=1-2=-1[/tex]